Question

An alloy of gold (Au) and cadmium (Cd) crystallises with a cubic structure in which gold atoms occupy the corners and cadmium atoms fit into the face centres. What is the formula of this alloy?

Answer 1

The alloy has a cubic structure. 

Gold (Au) atoms occupy the corners of the unit cell.

Cadmium (Cd) atoms fit into the face centers of the unit cell.

Gold atoms (Au): There are 8 corners in a cubic unit cell, and each corner atom is shared by 8 unit cells.

Therefore, the contribution of gold atoms to the unit cell is 1 atom.

Cadmium atoms (Cd): There are 6 face centers, and each face-centered atom is shared by 2 unit cells.

Therefore, the contribution of cadmium atoms to the unit cell is 3 atoms.

In the unit cell, there is 1 gold atom (Au) and 3 cadmium atoms (Cd).

∴ The formula of the alloy is AuCd₃.